This question has been answered here:

From where (in space-time) does Hawking radiation originate?

Note particularly this comment:

" The way that the information is imprinted in the horizon is crazy--- its not that the photon is interacting with other stuff frozen on the horizon, its that the horizon itself is jiggling thermally, and the jiggles themselves are the infalling photon and the infalling matter. They contain the entire physics of the infalling matter. This is the holographic idea. When the infalling photon gets close, it is described more and more by BH jiggles (rather than cosmological jiggles), and these jiggles obey an information preserving field theory, at least when extremal."

This question has been answered here by Ron:

From where (in space-time) does Hawking radiation originate?

Note particularly this comment to Ron's answer:

" The way that the information is imprinted in the horizon is crazy--- its not that the photon is interacting with other stuff frozen on the horizon, its that the horizon itself is jiggling thermally, and the jiggles themselves are the infalling photon and the infalling matter. They contain the entire physics of the infalling matter. This is the holographic idea. When the infalling photon gets close, it is described more and more by BH jiggles (rather than cosmological jiggles), and these jiggles obey an information preserving field theory, at least when extremal."